New Statistical Methods for Evaluating Brain Functional Connectivity

Abstract

The human brain functions through the coordination of a complex network of billions of neurons. This network, when defined by the functions it dictates, is known as functional brain connectivity. Associating brain networks with clinical symptoms and outcomes has great potential for shaping future work in neuroimaging and clinical practice. Resting-state functional magnetic resonance imaging (rfMRI) has commonly been used to establish the functional brain network; however, understanding the links to clinical characteristics is still an ongoing research question. Existing methods for analysis of functional brain networks, such as independent component analysis and canonical correlation analysis, have laid a good foundation for this research; yet most methods do not directly model the node-level association between connectivity and clinical characteristics, and thus provide limited ability for interpretation. To address those limitations, this dissertation research focuses on developing efficient methods that identify node-level associations to answer important research questions in brain imaging studies.

In the first project, we propose a joint modeling framework for estimating functional connectivity networks from rfMRI time series data and evaluating the predictability of individual's brain connectivity patterns using their clinical characteristics. Our goal is to understand the link between clinical presentations of psychiatric disorders and functional brain connectivity at different region pairs. Our modeling framework consists of two components: estimation of individual functional connectivity networks and identifying associations with clinical characteristics. We propose a model fitting procedure for jointly estimating these components via the alternating direction method of multipliers (ADMM) algorithm. The key advantage of the proposed approach lies in its ability to directly identify the brain region pairs between which the functional connectivity is strongly associated with the clinical characteristics. Compared to existing methods, our framework has the flexibility to integrate machine learning methods to estimate the nonlinear predictive effects of clinical characteristics. Additionally, jointly modeling the precision matrix and the predictive model estimates provides a novel framework to accommodate the uncertainty in estimating functional connectivity.

In the second project, we focus on a scalar-on-network regression problem which utilizes brain functional connectivity networks to predict a single clinical outcome of interest, where the regression coefficient is edge-dependent. To improve estimation efficiency, we develop a two stage boosting algorithm to estimate the sparse edge-dependent regression coefficients by leveraging the knowledge of brain functional organization. Simulations have shown the proposed method has higher power to detect the true signals while controlling the false discovery rate better than existing approaches. We apply the proposed method to analysis of rfMRI data in the Adolescent Brain Cognitive Development (ABCD) study and identify the important functional connectivity sub-networks that are associated with general cognitive ability.

In the third project, we extend scalar-on-network regression via boosting in the second project by relaxing the homogeneity constraints within the prespecified functional connectivity networks. We adopt deep neural networks (DNN) to model the edge-dependent regression coefficients in light of the edge-level and node level features in the brain network, as well as the well-known brain functional organization. In addition, the proposed DNN-based scalar-on-network regression has the flexibility to incorporate the signal pattern from other imaging modalities into the model. We develop an efficient model fitting method based on ADMM. The proposed method is evaluated and compared with existing alternatives via simulations and analysis of rfMRI and task fMRI data in the ABCD study.